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Pengfei Yu, Shu Xiao, Xiaoyun Xin, et al. dynamic gene regulationSpatiotemporal clustering of the epigenome reveals rules of

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Method

Spatiotemporal clustering of the epigenome revealsrules of dynamic gene regulationPengfei Yu,1,2,5 Shu Xiao,1,2,5 Xiaoyun Xin,3,6 Chun-Xiao Song,4,6 Wei Huang,2,6

Darina McDee,2 Tetsuya Tanaka,2 Ting Wang,3 Chuan He,4 and Sheng Zhong1,2,7

1Department of Bioengineering, University of California, San Diego, California 92093, USA; 2Institute for Genomic Biology, University

of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; 3Department of Genetics, Washington University in St. Louis,

St. Louis, Missouri 63108, USA; 4Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA

Spatial organization of different epigenomic marks was used to infer functions of the epigenome. It remains unclear whatcan be learned from the temporal changes of the epigenome. Here, we developed a probabilistic model to cluster genomicsequences based on the similarity of temporal changes of multiple epigenomic marks during a cellular differentiationprocess. We differentiated mouse embryonic stem (ES) cells into mesendoderm cells. At three time points during thisdifferentiation process, we used high-throughput sequencing to measure seven histone modifications and var-iants—H3K4me1/2/3, H3K27ac, H3K27me3, H3K36me3, and H2A.Z; two DNA modifications—5-mC and 5-hmC; andtranscribed mRNAs and noncoding RNAs (ncRNAs). Genomic sequences were clustered based on the spatiotemporalepigenomic information. These clusters not only clearly distinguished gene bodies, promoters, and enhancers, but alsowere predictive of bidirectional promoters, miRNA promoters, and piRNAs. This suggests specific epigenomic patternsexist on piRNA genes much earlier than germ cell development. Temporal changes of H3K4me2, unmethylated CpG, andH2A.Z were predictive of 5-hmC changes, suggesting unmethylated CpG and H3K4me2 as potential upstream signalsguiding TETs to specific sequences. Several rules on combinatorial epigenomic changes and their effects on mRNA ex-pression and ncRNA expression were derived, including a simple rule governing the relationship between 5-hmC and geneexpression levels. A Sox17 enhancer containing a FOXA2 binding site and a Foxa2 enhancer containing a SOX17 binding sitewere identified, suggesting a positive feedback loop between the two mesendoderm transcription factors. These dataillustrate the power of using epigenome dynamics to investigate regulatory functions.

[Supplemental material is available for this article.]

An epigenome consists of chemical modifications and protein

variations to the DNA and histones, and some of these modifica-

tions and variations can be passed down to an organism’s offspring

(Bernstein et al. 2007). Epigenomes are dynamic, and epigenetic

modifications are associated with changes in gene expression

(Creyghton et al. 2010; Hawkins et al. 2011). Thus, the epigenome

adds an extra layer of information onto the genomic sequence and

enables a genome to dynamically orchestrate gene expression in

different cell types (Karlic et al. 2010; Maunakea et al. 2010). It is

argued that organismal development can be viewed as a pro-

gression of epigenomic states (Bernstein et al. 2007; Hawkins et al.

2010). To gain mechanistic support for this view, a number of

challenges have to be addressed. First, when presented with ge-

nome-wide distributions of epigenetic modifications at multiple

time points during a developmental or differentiation process,

how can we find the genomic (cis-) regulatory sequences that

regulate gene expression? What are the combinatorial functions of

epigenetic modifications and regulatory sequences? Here, we

present experimental data and a probabilistic model that utilizes

the temporal changes of the epigenome to annotate the regula-

tory sequences. This approach classifies regulatory sequences

by their temporal epigenomic patterns, and thus it can identify

subclasses of cis-regulatory sequences with different regulatory

functions.

Two types of associations were observed between the epi-

genome and gene expression. First, in a given cell type, the tran-

scription levels of different genes are associated with the epi-

genomic modifications in the genomic neighborhoods of these

genes. In other words, without changing cell types, epigenomic

modifications at different chromosomal locations are indicative of

the relative abundance of RNAs transcribed from these locations

(Fig. 1A, spatial correlation [S]; Karlic et al. 2010). Second, for

a given gene, the temporal change in its expression during a de-

velopmental or differentiation process is associated with temporal

epigenomic changes (Fig. 1A, temporal correlation [T]; Rada-

Iglesias et al. 2011). The first type of association facilitated the use

of invariant epigenomic signatures in a static cellular condition to

annotate genomic features (Ernst and Kellis 2010). However, genes

are dynamically regulated in nearly all biological processes. It is

important to incorporate the dynamic aspect of gene regulation

into the annotation of the regulatory sequences. Here, we jointly

model the position effect and the temporal effect of the epi-

genome, thus achieving ab initio identification and functional

annotation of regulatory sequences.

The regulatory functions of a number of epigenetic mod-

ifications remain elusive. A case in point is DNA hydroxy-

methylation (Wyatt and Cohen 1952). Methylated cytosine

(5-mC) can be converted to an oxidized form 5-hydroxy-

methylcytosine (5-hmC) by a family of ten-eleven translocation

(TET) proteins (Tahiliani et al. 2009; Ito et al. 2010). In embryonic

stem (ES) cells, 5-hmC is enriched in gene bodies of actively tran-

5These authors contributed equally to this work.6These authors contributed equally to this work.7Corresponding authorE-mail [email protected] published online before print. Article, supplemental material, and pub-lication date are at http://www.genome.org/cgi/doi/10.1101/gr.144949.112.

352 Genome Researchwww.genome.org

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scribed genes (Wu et al. 2011a), promoters of inactive genes (Ficz

et al. 2011; Pastor et al. 2011; Wu et al. 2011a), and active en-

hancers (Stroud et al. 2011). These seemingly conflicting data are

thought-provoking for analyzing epigenetic modifications in a

combinatorial manner, such that the function of each modifica-

tion is investigated in the context of other modifications as well as

the underlying genomic sequence. By modeling the co-appearance

of different epigenetic modifications in each cell type, a pioneering

method demonstrated the power in predicting different genomic

features, including enhancers and genes (Ernst and Kellis 2010).

However, epigenomic co-appearance in static cell types does not

reveal all epigenetic mechanisms of gene regulation. Two major

questions remain unsolved. First, what are the upstream signals

that guide specific epigenomic modifications, such as 5-hmC, to

appear in specific genomic regions? Second, the regulatory func-

tions for several epigenomic marks, including 5-hmC and H2A.Z,

remain elusive. New ideas for combinatorial epigenomic analyses

beyond the co-appearance in static cell types are needed. A natural

extension in this direction is to utilize a dynamic process in which

both the epigenome and the transcriptome have changes. Ideally,

we need some methods that can capture combinatorial patterns of

temporal epigenomic changes and correlate them with gene ex-

pression changes.

A major difficulty in analyzing epigenomic dynamics lies in

the asynchronous nature of epigenomic changes in different ge-

nomic regions. Suppose a type of epigenomic change, for example,

the induction of H3K4me1 and 5-hmC, is a recurring pattern

shared by many genomic regions. Such a pattern can be difficult to

find because different genomic regions can accumulate either

modification at different times. Furthermore, the corresponding

changes in gene expression are not synchronized, making it dif-

ficult to associate epigenomic dynamics with gene expression

changes. To reveal the hidden rules of epigenomic dynamics

and gene expression, we developed a spatiotemporal clustering

model. This model clusters genomic regions by shared epigenomic

changes but does not require the changes to be synchronized

among a cluster of genomic regions. This was achieved by allowing

each region to have its own time-specific epigenomic states and then

integrating out the time of transition between the epigenomic

states in the clustering model.

To investigate the functions of epigenetic modifications in

a dynamic process, we differentiated mouse ES cells into mesen-

doderm cells (Yasunaga et al. 2005), the common precursor of

mesoderm and endoderm. At three time points during this differ-

entiation process, we mapped the genomic distributions of nine

epigenetic modifications, including DNA methylation (5-mC),

hydroxymethylation (5-hmC), histone variant H2A.Z, and histone

modifications H3K4me1, H3K4me3, H3K27ac, H3K27me3, and

H3K36me3. At the same time points, we also assayed the expres-

sion of small noncoding RNAs (ncRNAs) and total RNAs (Supple-

mental Fig. S1). Our model-based analysis of these temporal data

revealed several fundamental properties of epigenome dynamics,

characterizing regulatory roles for functionally elusive epigenomic

modifications. As an analogy to the sequence ‘‘rules’’ of gene reg-

ulation (Buchler et al. 2003; Beer and Tavazoie 2004), these dis-

coveries may provide epigenomic ‘‘rules’’ of gene regulation.

Results

A model for genome annotation using temporalepigenomic data

We developed a probabilistic model to annotate the genome using

temporal epigenomic data. Two main features of this model in-

clude explicit treatment of combinatorial epigenomic changes and

detecting similar but asynchronous epigenomic changes in dif-

ferent genomic segments.

As input data to the model, the genome is represented as

consecutive genomic segments, with a typical segment size of 200

nucleotides (nt) (for the impact of segment sizes, see Supplemental

Fig. S5). Each segment is associated with the time-specific in-

tensities of a set of epigenetic modifications. The model clusters

the genomic segments, such that each cluster shares a similar

combination of epigenetic modifications as well as their temporal

changes. We call the combination of epigenetic modifications

shared by a cluster of genomic segments at a given time an epi-

genomic state. Each cluster represents a time-series of related epi-

genomic states. Essentially this model assigns epigenomic states

based on time-series epigenomic data.

Figure 1. The genomic annotation based on the time-course epi-genomic data (GATE) model. (A) Two types of correlations between theepigenome and gene expression. Spatial correlation (S) examines dif-ferent genes in a fixed cell type, and temporal correlation (T) examinesdifferent differentiation stages or cell types for a fixed gene. Spatial cor-relation is often much more pronounced than temporal correlation. (B–C )GATE models the genome as equal-sized genomic segments, and eachsegment is associated with temporal epigenomic data. The model as-sumes that there are shared temporal epigenomic patterns among dif-ferent genomic segments. GATE is a hierarchical model. The top layer isa finite mixture model for clustering genomic segments. The bottom layermodels the temporal changes within each cluster as a hidden Markovmodel. The hidden variables (circles) are binary variables, indicating thetime of a change of regulatory activities. Emitted (vertical arrows) from thehidden variable are the intensities of each epigenomic mark.

Genome Research 353www.genome.org

Spatiotemporal clustering of the epigenome


We call this model genomic annotation using temporal epi-

genomic data (GATE). GATE is a hierarchical model (Pearl 1985)

with two layers (Fig. 1B). The top layer is a finite mixture model

(FMM) (Equihua 1988), in which each component of the mixture

represents a cluster of genomic segments that share temporal epi-

genomic patterns. Without considering the time factor, each

component (cluster) degenerates into a set of genomic segments

sharing an epigenomic state. The bottom layer models the epi-

genomic data in each cluster. Each cluster is modeled as a hidden

Markov model (HMM) (Durbin et al. 1998) that represents the

temporal changes of epigenetic modification intensities. The hid-

den states are binary activity states (inactive and active), which are

allowed to change with respect to time. For example, if an en-

hancer changes from an active enhancer into an inactive enhancer

during differentiation, the hidden states for this enhancer would

change from 0 (inactive) to 1 (active). In a differentiation process,

state 0 can be interpreted as the initial state before differentiation

(undifferentiated [U]), whereas state 1 can be regarded as the other

state in differentiated cells (differentiated [D]). The observed data

are the epigenetic modification intensities for each genomic seg-

ment at every time point (Fig. 1B). The sequencing reads from

chromatin immunoprecipitation followed by sequencing (ChIP-

seq) experiments for each epigenetic modification on a genomic

segment are modeled with a Poisson distribution, with the Poisson

parameter reflecting the cluster and time-dependent epigenomic

state. Thus, GATE has been completely specified as a generative

probabilistic model (see Methods). In short, GATE is a finite mix-

ture of HMMs. Distinguishing itself from a previous method that

predicts chromatin states based on static epigenetic data (Ernst

and Kellis 2010), GATE models epigenomic data as a dynamic

continuum and directly utilizes temporal information to anno-

tate epigenomic states. This feature facilitates the discovery of cis-

regulatory sequences and the annotation of their regulatory

functions (Supplemental Fig. S6).

We implemented an expectation–maximization (EM) method

(Dempster et al. 1977) to estimate model parameters from data

(Supplemental Fig. S1; Supplemental Methods). At every maximi-

zation step, we embedded a Baum-Welch algorithm (Durbin et al.

1998) to estimate the HMM parameters. We provide GATE as a fully

documented program at http://biocomp.bioen.uiuc.edu/GATE.

GATE was tested with simulated cell differentiation processes

(Supplemental Data 1; Supplemental Tables S2–S4).

Epigenomic landscape during the differentiation of ES cellsto mesendoderm

Mesendoderm is the diverging point of definitive endoderm and

mesoderm (Yasunaga et al. 2005), which represents an important

cell lineage besides the neural lineage (ectoderm) during the early

stages of ES cell differentiation. We differentiated mouse ES cells to

mesendoderm using Activin and a previously described culture

medium (Yasunaga et al. 2005). On the sixth day of differentiation,

almost all cells exhibited typical mesendoderm morphology and

expressed mesendoderm protein Goosecoid (GSC) (Blum et al.

1992) and endoderm protein SOX17 (Supplemental Fig. S2A; Kanai-

Azuma et al. 2002). Pluripotency genes Pou5f1(also known as Oct4),

Sox2, and Nanog were down-regulated, whereas endoderm and

mesoderm genes Gsc, Chordin, Foxa2, Sox17, Lim1, and Hnf4 were

up-regulated (Supplemental Fig. S2B).

We measured a total of nine epigenomic marks at three time

points (day 0, 4, and 6) during the differentiation process. These

marks included seven histone modifications or variants (H3K4me1/

2/3, H3K27ac, H3K27me3, H3K36me3, and H2A.Z), which were

assayed by ChIP-seq (Xiao et al. 2012). We supplemented the his-

tone data with two types of DNA modifications, including 5-hmC

by chemical labeling and pull-down followed by sequencing

(5-hmC-seq) (Song et al. 2011) and 5-mC by both methylated DNA

immunoprecipitation followed by sequencing (MeDIP-seq) and

DNA digestion by methyl-sensitive restriction enzymes followed

by sequencing (MRE-seq) (Maunakea et al. 2010). The 5-hmC pull-

down specifically used the chemical property of the hydroxyl-group

and thus was efficient to distinguish 5-hmC from 5-mC (Song et al.

2011). MeDIP-seq was representative of 5-mC, and MRE-seq was rep-

resentative of unmethylated CpGs (uCpGs) (Maunakea et al. 2010).

To analyze the transcriptome, we sequenced ncRNAs using

the Illumina Small RNA Sample Preparation procedure followed by

sequencing (Illumina 2010b) and mRNAs using RNA-seq (Mortazavi

et al. 2008) at the same three time points. Taken together, 36 se-

quencing data sets composed of 1.94 billion 75-nt or 100-nt

uniquely alignable sequencing reads were generated.

These data allowed us to estimate that 11.5% of the mouse ge-

nome is associated with at least one type of epigenetic modification

in undifferentiated ES cells. Nearly half of these regions (5.60% of the

genome) exhibited significant changes in at least one epigenetic

modification during differentiation. About 1.92% of the genome was

transcribed into mRNAs in ES cells, and 0.43% of the genome

exhibited change of mRNA expression levels during differentiation.

Spatiotemporal clustering of epigenomic states

GATE clusters genomic segments based on both spatial distribu-

tions of epigenomic modifications and temporal changes of these

modifications. Applying GATE to the ‘‘ES cell to mesendoderm’’

differentiation data set, we initially obtained 55 clusters, consis-

tent with the previously estimated number of chromatin states

(Ernst and Kellis 2010). These clusters formed 14 larger groups

(Supplemental Fig. S3). Twelve of the 14 groups showed epi-

genomic characteristics that are typical to gene bodies, promoters,

and enhancers. For example, groups 2, 3, 6, and 9 shared enhancer

characteristics, including low H3K36me3, high H3K4me1 in either

undifferentiated (Fig. 2A, U) or differentiated states (D), and either

high H3K27me3 or high H3K27ac (Fig. 2, vertical green bar).

Groups 1b, 5, 8, and 12 shared promoter characteristics, includ-

ing high H3K4me3 and low H3K36me3 (red bar). Groups 1a, 4, 10,

and 11 shared high levels of H3K36me3, which was associated

with gene bodies (Fig. 2, blue bar; Kolasinska-Zwierz et al. 2009;

Schwartz et al. 2009).

By assigning clusters as promoter, enhancer, gene body, and

repeat clusters (Fig. 2, red, green, blue, and gray bars), we turned

the unsupervised spatiotemporal epigenomic clusters into pre-

dictions of different genomic features. To check these predictions,

we compared the locations of the genomic segments in every

cluster to their nearest genes. Indeed, the relative locations of ge-

nomic segments in each cluster corroborated the unsupervised

predictions (Supplemental Fig. S4). Chromosome 11 was randomly

chosen for quantifying the prediction accuracies. The sensitivities

for detecting promoters increased from 0% to 60% when the false-

positive rate (1 � specificity) increased from 0% to 0.25% (Fig. 3B).

Similar tradeoffs between sensitivity and specificity were found for

gene body predictions (Fig. 3C). These quantities reinforced the visual

impression (Supplemental Fig. S4) that spatiotemporal clusters cor-

relate with different genomic features. Changing the input size of

genomic segments from 200 nt to 100 nt did not change any quali-

tative characteristics of the clustering results (Supplemental Fig. S5).

Yu et al.



Spatiotemporal epigenomic clusters are predictiveof transposons, bidirectional promoters, microRNApromoters, and PIWI RNAs

Not only did the spatiotemporal epigenomic clusters predict usual

genomic features such as enhancers, promoters, and gene bodies,

unexpectedly these clusters were also capable of predicting ge-

nomic features, including repeats, bidirectional promoters (Lin et al.

2007; Hakkinen et al. 2011), microRNA (miRNA) promoters (Marson

et al. 2008), and PIWI RNAs (piRNAs) (Thomson and Lin 2009).

Two groups (groups 13 and 14) exhibited unfamiliar epi-

genomic characteristics, including high H3K36me3 in parallel

with high H3K27me3. These clusters did not locate in gene bodies

or promoters (Supplemental Fig. S4). They contained the highest

proportions of repeats among all 55 clusters (P = 5.45 3 10�37,

Fisher’s exact test) (Fig. 2B, ‘‘repeats’’ column). ncRNA expression

showed that groups 13 and 14 corresponded to transcribed and

silenced repeat sequences (Fig. 2B, ncRNA). These data suggest

a distinct spatiotemporal epigenomic signature for repeats and

transposons.

Figure 2. Epigenomic clusters. (A) Average intensities of each epigenomic mark (column) in each cluster (row). The model allows each sequencesegment to have two activity states, denoted as undifferentiated (U) and differentiated (D). The model assumes that each cluster has a shared meanintensity for each epigenomic mark at either activity state. These mean intensities are plotted in this matrix and are color-coded. Clusters with similarintensities were merged into larger clusters (groups) (for the merging procedure, see Supplemental Fig. S3). Based on the epigenomic patterns, the groups wereassigned with representative names, including promoters, enhancers, genes, and repeats (vertical color bars). Consistent intensity changes across multipleclusters in a group are highlighted (red circles). (B) Fold enrichment of genomic and epigenomic features (column) in each cluster (row). Fold enrichment wascalculated as the ratio between the average signal of a cluster to the average signal of all clusters. mRNA indicates transcription levels of nearest genes, derivedfrom RNA-seq data; ncRNA, transcription levels of the genomic segment in each cluster, derived from ncRNA-seq data; CpG, CpG density; P300, EP300 (alsoknown as p300) binding intensity; PolII, PolII binding intensity; and repeats, repeat density. Significant temporal changes are highlighted (orange circles).




Bidirectional promoters were strongly enriched in group 8

(clusters 19, 12, 48; P = 3.9 3 10�290) (Fig. 3A). A simple but

powerful classifier for identifying bidirectional promoters can be

built based on the clusters. Based on whether a genomic segment

belongs to cluster 19, one can reach 80% sensitivity with a speci-

ficity of 99.6% (Fig. 3D). Besides bidirectional promoters, miRNA

promoters were also enriched in specific clusters, including clus-

ter 28 (P = 6.96 3 10�28, Fisher’s exact test) and cluster 52 (P =

1.51 3 10�11, Fisher’s exact test) (Supplemental Fig. S7A). Thus,

through unsupervised clustering, GATE revealed distinct spa-

tiotemporal epigenomic patterns in several specific types of

promoters.

PiRNAs and PIWI proteins were discovered in germ cells

(Thomson and Lin 2009) and were thought to be silenced in ES

cells. Unexpectedly, piRNAs were specifically enriched in cluster 11

(P = 3.08 3 10�16, Fisher’s exact test) and cluster 28 (P = 2.05 3

10�6, Fisher’s exact test) (Supplemental Fig. S7B). As a control, in

cluster 11 where piRNA was strongly enriched (9.53-fold more

enriched than expected), miRNAs were depleted (0.89-fold less

than expected). Thus piRNAs and miRNAs had different tem-

poral epigenomic characteristics. These data suggest that even

though piRNAs were produced and func-

tional in germ cells, specific epigenomic

patterns were formed on piRNA genes

much earlier than germ cell develop-

ment. PiRNA genes may be epigenetically

prepared for activation in ES cells.

The distinct epigenomic character-

istics in ES cells opened the possibility

that a subset of piRNAs is produced in

ES cells. Indeed, a cluster of piRNA

genes (piRNA cluster) on chromosome

5 was clearly expressed (Supplemental

Fig. S7C). Moreover, the expression of

this piRNA cluster was specifically in-

duced in undifferentiated ES cells (Supple-

mental Fig. S7C, days 0, 4, 6). As a control,

Sgsm1, the neighboring gene to this

piRNA cluster, showed a slight increase in

expression during differentiation (Sup-

plemental Fig. S7C). Even more strikingly,

Piwil2 (also known as Mili), a mouse

ortholog of the Drosophila PIWI gene, is

expressed in ES cells, and its expression

decreased below a detectable level 4 d af-

ter differentiation (Supplemental Fig.

S7D). The consistent inductions of

piRNAs and the Piwil2 gene in un-

differentiated ES cells further entertained

the hypothesis that some piRNAs were

produced not only in germ cells.

Combinatorial temporal changesof epigenomic modifications

There were large differences among the

nine epigenomic modifications regarding

their temporal changes. The most sta-

ble modification was H3K36me3, which

showed little change in all groups. The

other eight modifications showed cluster-

specific temporal changes (Fig. 2).

Gene body groups showed three types of combinatorial

changes. The first type was represented by coordinated decreases of

H3K27ac, H3K4me1/2, H2A.Z, and 5-hmC and an increase in CpG

methylation (Fig. 2, red circles in group 4). These coordinated

epigenomic changes did not clearly influence mRNA expression

(Fig. 2B, mRNA) but were associated with strong up-regulation of

ncRNAs (Fig. 2B, ncRNA). The second combination was decreases

of H3K27ac and H3K4me2/3 (red circles, group 11), which were

associated with down-regulation of both mRNAs and ncRNAs

(orange circles). The third combination was coordinated increases

of H3K4me1/2 and 5-hmC, which corresponded to up-regulation

of ncRNAs (groups 1a and 10).

All promoter groups shared increases of H3K4me1/2, H2A.Z,

5-hmC, and 5-mC together with a decrease in CpG methylation.

Interestingly, this recurrent combinatorial pattern itself was

not sufficient to induce gene expression changes. However,

when this pattern was further combined with a decrease in

H3K4me3, it was associated with down-regulation of ncRNAs

(Fig. 2, group 1b).

Enhancer groups showed four types of combinatorial

changes. The first type was an increase in CpG methylation, which

Figure 3. Predicting genomic features. (A) Distribution of bidirectional promoters in the 55 epi-genomic clusters. Fold enrichment indicates the ratio between the percentage of bidirectional pro-moters in a cluster and the average percentage of all clusters. (*) P < 10�60; (**) P < 10�90. (B–D)Accuracies of predicting genomic features as measured by receiver operating characteristic (ROC)curves. AUC indicates area under the curve. Promoters were predicted by groups 1b, 5, 8, and 12 (P <2.2 3 10�16, Wilcoxon test). Gene bodies were predicted by groups 1a, 4, 10, and 11 (P < 2.2 3 10�16).Bidirectional promoters were predicted by cluster 19 (P < 2.2 3 10�16). (Insets) Details of the highspecificity regions. (E ) A predicted bidirectional promoter and a regular promoter. Along a fraction ofchromosome 11, each genomic segment is colored by the cluster it belonged to. The stretch of DNAbelonging to cluster 19 (yellow) corresponded to a bidirectional promoter.

Yu et al.



correlated with down-regulation of ncRNAs (red and orange

circles, group 6). The second combination was an increase in

H3K27ac and decreases in H3K27me3 and 5-mC, which correlated

with up-regulation of mRNAs and ncRNAs. The third type was

coordinated decreases of H3K27ac, H3K4me1/2, H2A.Z, and 5-hmC

together with an increase in 5-mC, which correlated with down-

regulation of mRNAs and ncRNAs (group 9). The last type was

coordinated decreases of H3K27ac and H3K4me3 together with

a 5-mC increase, which correlated with down-regulation of mRNAs

and ncRNAs (Fig. 2, group 7).

Both transcribed and silenced repeats showed coordinated

decreases in H3K27me3, 5-hmC, and 5-mC (especially non-CpG

methylation [mCpH]), which correlated with up-regulation of

transcription (Fig. 2, ncRNA).

Recurrent themes of epigenomic and transcriptome changes

Recurrent themes appeared in the majority of the spatiotemporal

clusters. These recurring patterns may represent basic properties of

temporal gene regulation by the epigenome.

First, combinatorial epigenomic changes are prevalent. In

every case except one, we observed combinatorial changes of three

to seven epigenomic modifications. Furthermore, different geno-

mic features (promoters, enhancers, genes, and repeats) have dif-

ferent combinations of temporal changes.

Second, combinatorial patterns of epigenomic changes are

predictive of gene expression changes (Fig. 1A, temporal axis).

While gene expression data were not used in clustering epigenomic

data, the epigenomic clusters clearly distinguish gene groups with

different temporal expression changes (Fig. 2).

Third, almost all combinatorial epigenomic changes corre-

spond with changes in ncRNA expression levels. The direction of

ncRNA expression changes was not associated with the changes in

any single epigenomic modification but was strongly predictable

by combinatorial changes (see Fig. 6).

Fourth, epigenomic changes in enhancers instead of

promoters are indicative of mRNA expression changes. This

reconciles previous observations that temporal epigenomic

changes were poorly correlated with gene expression changes

during cell differentiation (Wu et al. 2011b) by reproducing such

results in promoter regions with more epigenomic modifica-

tions; but also it points out the importance of epigenomic

changes in enhancers. Consistently, human ChIP-chip anal-

ysis showed enhancer associated modifications, including

H3K27ac and H3K4me1, had greater dynamic changes than

other modifications during ES cell differentiation (Hawkins et al.

2011).

Fifth, all assayed modifications except H3K36me3 have

robust temporal changes in multiple genomic features (pro-

moters, enhancers, gene bodies, and repeats). The robust and

recurrent temporal changes appeared not only in genomic re-

gions where the epigenomic modifications were abundant, but

also in genomic regions where the modification levels were

low. Previously, H3K4me1 was associated with enhancers and

H3K4me3 and H2A.Z were associated with promoters due to

their abundance in these regions. However, H3K4me1 showed

reliable changes not only in enhancers, but also in promoters

and gene bodies where its modification level was low. Similarly,

H3K4me3 (group 7) and H2A.Z (group 9) showed reliable

changes in enhancers. These data may suggest regulatory func-

tions of epigenomic modifications in previously ignored geno-

mic regions.

Temporal changes of H3K4me2, mCpH, and H2A.Zare predictive of DNA hydroxymethylation

It remains unknown what guides TET enzymes to specific parts of

the genome to convert 5-mC to 5-hmC. To explore the upstream

signals that might specify where in the genome 5-mC should be

converted to 5-hmC, we asked if there were any epigenomic

modifications that correlate with 5-hmC in terms of temporal

changes. Across all 55 epigenomic clusters (Fig. 2), the temporal

changes of 5-hmC were on average most correlated with

H3K4me2, uCpG (measured by MRE-seq), H3K4me1, and H2A.Z

(Supplemental Fig. S8). Next, we checked the temporal correlations

between 5-hmC and every other assayed epigenomic mark on

every genomic segment (200-nt window). On 78.1% of the geno-

mic segments, the temporal correlations between 5-hmC and

H3K4me2 were larger than 0.8 (P < 10�300) (Supplemental Fig.

S9B). Strong temporal correlations between 5-hmC and uCpG,

5-hmC and H4K4me1, and 5-hmC and H2A.Z were also observed

(Supplemental Fig. S9E,9F). In contrast, H3K4me3 and H3K36me3

did not show large temporal correlations with 5-hmC. By catego-

rizing genomic segments by their clusters, promoter segments

showed the strongest temporal correlations between 5-hmC

and H3K4me2, uCpG, and H2A.Z (Supplemental Fig. S9). These

data indicate strong associations between the di- and mono-

methylation of H3K4 and hydroxylmethylation of nearby cyto-

sines. The exchange of histone variants H2A and H2A.Z may also

associate with 5-hmC synthesis.

The temporal changes of uCpG and 5-hmC were strongly

correlated (Supplemental Fig. S9K). Two scenarios can fit these

data. First, the uCpG was generated by a cytosine demethyla-

tion preprocess that involves the conversion of 5-mC to 5-hmC

(Bhutani et al. 2011). In other words, the same cytosine is con-

verted from 5-mC into 5-hmC and then into C (same cytosine

hypothesis). Alternatively, uCpG signals TET enzymes to the ge-

nomic neighborhood to convert neighboring 5-mC into 5-hmC

(neighbor hypothesis). If the same cytosine hypothesis is true, we

would predict that 5-mC and 5-hmC are anti-correlated during ES

cell differentiation. However, temporal changes of 5-mC did not

anti-correlate with 5-hmC changes (Supplemental Fig. S9M). More

genome segments had the same direction of 5-mC changes and

5-hmC changes than expected at random (P < 10�200) (Supple-

mental Fig. S9M, dashed line). These data are inconsistent with the

same cytosine hypothesis. Conversely, TET1 contains a Znf_CXXC

domain that interacts with uCpG, which is in line with the

neighbor hypothesis.

We then explored the roles of mCpH. mCpH was reported in

oocytes without known functions (Tomizawa et al. 2011). ThesemCpHs were presumably due to high levels of de novo methylation

enzymes Dnmt3a/b in oocytes (Lees-Murdock et al. 2005). The

simultaneous increase of 5-mC and decrease of CpG methylation

in the same promoters (see Fig. 6; Supplemental Fig. S4) suggest

de novo mCpH. This is consistent with the increased expression

levels of DMNT3b during guided differentiation of ES cells toward

mesendoderm cells (Supplemental Fig. S9N). Temporal changes ofmCpH were strongly correlated with 5-hmC changes (Supple-

mental Fig. S9D), suggesting the genomic segments undergoingmCpH were also experiencing hydroxymethylation. Comple-

mentary to these data, 5-hmC level was most enriched in low

CpG regions in ES cells (Yu et al. 2012). In summary, temporal

changes of H3K4me1/2, mCpH, and H2A.Z are predictive of 5-hmC

changes throughout the mouse genome. These temporal correla-

tions do not provide any causal information, but they may help to




prioritize some hypotheses for future biochemical analyses of

5-hmC pathways.

H2A.Z is predictive of gene expression in a context-specificmanner

Epigenomic marks were thought to be predictive of gene expres-

sion levels in a context-independent manner (Karlic et al. 2010).

The main support for this idea was that the linear model using

epigenomic marks to predict expression can be learned from CD4+

T cells and then applied to other types of T cells (Karlic et al. 2010).

To see if this theory holds during ES cell differentiation, we cor-

related the model-learned epigenomic modification levels to gene

expression levels (Supplemental Fig. S10). Consistent with pre-

vious thoughts, some epigenomic marks were correlated with

gene expression in a context-independent manner, in the sense

that these correlations persist in different genomic locations (en-

hancers, promoters, etc.) and in different differentiation states.

Such context-independent epigenomic marks included H3K36me3,

H3K27ac, and 5-mC. However, several epigenomic marks showed

context-specific influence on mRNA expression. Promoter

H3K4me3 was correlated with mRNA expression, but enhancer

H3K4me3 was not (Supplemental Fig. S10). Promoter H2A.Z was

not correlated with mRNA expression in undifferentiated ES

cells (Pearson correlation < 0), but promoter H2A.Z was strongly

correlated with mRNA expression after differentiation (Pearson

correlation = 0.83) (Supplemental Fig. S10, panel H2A.Z). Thus,

epigenomic marks, although associated with gene expression,

can have different directions of association in different cellular

contexts.

A unified model for 5-hmC’s effects on gene expression

The effects of 5-hmC on gene expression remain unclear. The

difficulty of clarifying 5-hmC’s effects lies, at least in part, in the

seemingly conflicting data. On the one hand, promoter 5-hmC

levels were anti-correlated with gene expression levels in both

undifferentiated and differentiated ES cells (Fig. 4A,B; Supple-

mental Fig. S10, panel 5-hmC). This may suggest 5-hmC as a re-

pressive mark. On the other hand, enhancer 5-hmC had a weak

positive correlation with gene expression (Fig. 4C,D; Supplemental

Fig. S10, panel 5-hmC), which may indicate an activation role. Is

there a simple model that can accommodate all these data and il-

lustrate 5-hmC’s effects on gene expression? We identified a model

by looking at temporal changes of 5-hmC.

5-hmC were concentrated on gene bodies in ES cells and were

shifted to promoters after differentiation (Figs. 4B; Supplemental

Fig. S11). These data are consistent with the recent discovery of

lower 5-hmC in promoters than in intragenic regions in ES cells

(Booth et al. 2012). However, the large increase of promoter 5-hmC

and the decrease of intragenic 5-hmC during ES cell differentiation

were not reported before. Enhancer concentration of 5-hmC was

Figure 4. A unified model showing the effects of 5-hmC on gene expression. (A–B) The average intensities of 5-hmC on predicted promoter groups (A)and enhancer groups (B) in three time points. Three thousand base pairs (bp) of flanking regions centered on the centers of the genomic segments of eachgroup are shown. (C,D) The expression levels of nearby genes for predicted promoter groups (C ) and enhancer groups (D). Mean and standard deviation(error bar) are shown for each time point. Whether 5-hmC increases above a critical threshold (horizontal line, A,B) correlates with the direction ofexpression changes. (FPKM) Fragments per kilobase of exon per million fragments mapped.

Yu et al.



increased during differentiation (Fig. 4D). The enrichment of

5-hmC in enhancers and promoters in differentiated cells provides

further support to the hypothesized regulatory role of 5-hmC (Ficz

et al. 2011; Pastor et al. 2011; Stroud et al. 2011; Wu et al. 2011a).

5-hmC showed either a substantial increase or a moderate

increase but showed no decrease in any enhancer clusters or pro-

moter clusters (Fig. 4B, D). In both promoters and enhancers,

a substantial increase of 5-hmC (Fig. 4A, promoter groups 5 and 12,

C, enhancer groups 2, 3, 6) inevitably resulted in induction of gene

expression. When 5-hmC did not substantially increase, nearby

genes would show decreasing expression. This was consistent with

both promoters (group 8) and enhancers (group 9). Similar anal-

yses on MeDIP-seq and MRE-seq data suggest that 5-mC did not

confound the observed effect of 5-hmC on gene expression (Sup-

plemental Fig. S12). Thus, a simple model can explain the re-

lationships between 5-hmC and gene expression during ES cell

differentiation. If 5-hmC increases above a critical value, gene

expression increases; otherwise, gene expression decreases. This

model states an association between 5-hmC and gene expression

changes, and it does not rule out additional epigenomic marks as

confounding factors.

Epigenomic states correlate with transcription networks

The GATE model infers epigenomic states of every genomic seg-

ment as undifferentiated (U) or differentiated (D), indicating when

a genomic segment may change its regulatory functions. Thus, the

GATE model provides a genome-wide view of the locations of

regulatory sequences as well as their time of activation. Such in-

formation may help to clarify the transcription network (Hawkins

et al. 2011). To explore this potential, we did a case study for three

mesendoderm genes: Fgf8, Sox17, and Foxa2. A set of group 3 en-

hancers were found in the introns and 39 intergenic regions of Fgf8

(Fig. 5A, yellow boxes). These enhancers were predicted to shift

from inactive to active epigenomic states (U/D). Transcription

factor binding sites (TFBSs) of GSC and IRF-1 appeared in these

enhancers (Fig. 5B,C). Both GSC and IRF-1 are key regulators of

mesendoderm differentiation (Blum et al. 1992; Bruce et al. 2007).

An isolated enhancer was identified ;50,000 nt upstream of the

Sox17 gene (Fig. 5D; Supplemental Fig. S12). Another enhancer was

found ;7000 nt upstream of the Foxa2 gene (Fig. 5E). By use of

epigenomic data, GATE suggested that both the Sox17 enhancer

and the Foxa2 enhancers shifted from inactive to active states

(Supplemental Fig. S13), which was in line with the increased ex-

pression of these genes (Fig. 5D,E, FPKM). A strong FOXA2 TFBS

appeared in the Sox17 enhancer, and a strong SOX17 TFBS appeared

in a Foxa2 enhancer. These data suggest a positive feedback loop

between Sox17 and Foxa2. Coincidently, a peak in a FOXA2 ChIP-

seq experiment in mouse liver (GEO accession no. GSM427089)

(MacIsaac et al. 2010) colocalized with the GATE-predicted Sox17

enhancer (Supplemental Fig. S14A, yellow bar). This is the strongest

peak (P-value < 10�6) in the 70,000-nt sequence neighborhood of

the Sox17 gene. Moreover, the predicted FOXA2 TFBS appeared at

the center of this peak (Supplemental Fig. S14A, insert). Reversely,

when Sox17 expression was induced in mouse ES cells, a strong peak

(fold change = 8.1, P < 2.5 3 10�7) of SOX17 ChIP-chip (GEO ac-

cession no. GSM470844) (Niakan et al. 2010) appeared ;7000 nt

upstream of the Foxa2 gene, colocalizing with the GATE-predicted

Foxa2 enhancer (Supplemental Fig. S14B). Moreover, the predicted

SOX17 TFBS located precisely at the center of this peak (Supple-

mental Fig. S14B, insert). These ChIP-seq/chip data reinforced the

GATE predicted feedback loop. This feedback loop can stabilize the

activation of two master transcription factors and thus may be es-

sential for mesendoderm differentiation.

DiscussionPrevious computational methods for analyzing epigenomes relied

primarily on spatial information of epigenomic marks. For exam-

ple, an HMM model was developed to annotate genomic se-

quences by colocalization of multiple epigenomic marks (Ernst

and Kellis 2010). GATE connects with the Ernst-Kellis model in

that with only one time point, GATE degenerates into a zero-order

HMM. Unlike the Ernst-Kellis model, though, GATE did not rely

on prior information about the arrangements of genomic fea-

tures. The unsupervised nature of GATE makes it capable of pre-

dicting the genomic features that were not included in a training

process. In the ES cell differentiation process, GATE predicted

bidirectional promoters, miRNA promoters, and piRNA genes

with high accuracies.

Temporal information is as important as spatial information

in studying epigenomic functions. A case in point is that although

TET was known to interact with the trithorax homolog MLL

(Tahiliani et al. 2009), the MLL targets H3K4me1/2 were not pur-

sued as a major clue for guiding TETs to specific genomic regions.

This was probably due to the lack of a very strong spatial correla-

tion between H3K4me1/2 and 5-hmC in any studied cell types.

Indeed, 5-hmC was enriched not only in enhancers where

H3K4me1/2 levels were high, but also in promoters (Yu et al. 2012),

CTCF binding sites (Yu et al. 2012), and gene bodies (Booth et al.

2012) where H3K4me1/2 levels were not necessarily high. How-

ever, temporal correlations between H3K4me1/2 and 5-hmC were

particularly strong, in that >85% of the genomic sequences had

the same direction of changes of H3K4me2 and 5-hmC (Supple-

mental Fig. S9B,E). This result prioritizes H3K4me1/2 and H3K4

methyltransferases as a candidate upstream signal for guiding TETs

to specific parts of the genome.

People questioned uCpG’s capability to attract TET1 (Frauer

et al. 2011), despite TET1 containing a zinc finger CXXC domain

that can bind uCpG (Tahiliani et al. 2009). Indeed, no genome-

wide mapping has showed strong overlaps of 5-hmC and uCpG.

Furthermore, the information content of CpG is small, making it

hard to believe that such a weak sequence signal can confer spec-

ificity to guide TET1. In this study, we reported striking temporal

correlations of 5-hmC and uCpG throughout the genome, high-

lighting the necessity of analyzing epigenome dynamics and

providing genome-wide data to support the role of uCpG in guid-

ing TET1. TET1’s interacting partner MLL contains a zinc finger

CXXC domain as well. Theoretically, the MLL–TET1–uCpGs three

way interaction can be a lot more stable than a two-way interaction

of a protein and its DNA recognition site (He et al. 2009). This

MLL–TET1–uCpGs interaction is reinforced by MLL’s roles to

methylate H3K4 and interact with methylated H3K4. These anal-

yses provide a model that uCpGs guide TET1 to specific genomic

locations by initiating self-reinforcing uCpGs–MLL–H3K4me1/

2–TET1 interactions.

It remains controversial whether 5-hmC predominantly ex-

ists in the CpG context. Stand bias analysis suggested presence of

5-hmC on CpH in ES cells (Ficz et al. 2011). However, this result

was not supported by single-base resolution mapping of 5-hmC

(Yu et al. 2012). We observed positive temporal correlations ofmCpH and 5-hmC in multiple genomic regions. Two scenarios fit

this observation. First, 5-hmC existed on CpH; alternatively, the

temporal changes of mCpH were associated with 5-hmC changes in




Figure 5. Predicted mesendoderm enhancers harbor transcription factor binding sites. Epigenomic clusters near the Fgf8 (A), Sox17 (D), and Foxa2 (E )genes. Genomic segments (colored bars) are marked by their cluster numbers on the left. Their variable widths indicate their activity states. A left-thin-right-fat bar indicates a change of the activity states. A strong GSC motif (B) and a strong IRF-1 motif (C ) appeared in predicted enhancer segments in the 39

and the intron of the Fgf8 gene. Both predicted enhancers showed changes of activities during the differentiation (left-thin-right-fat). A strong Foxa2 motifappeared in a predicted enhancer 50,000 bp upstream of the Sox17 gene (D). In turn, a strong Sox17 motif appeared in a predicted Foxa2 enhancer.(FPKM) Fragments per kilobase of exon per million fragments mapped.

Yu et al.



nearby CpGs. In promoters, uCpG levels measured by MRE-seq

often increased as 5-hmC levels increased, which suggests that

at least a subset of the newly converted 5-hmC in promoters were on

CpHs. These results suggest perhaps examining differentiated ES

cells may resolve the controversy of the presence of 5-hmC on CpHs.

Modeling and analyzing the temporal data facilitates the

discovery of context-specific functions of epigenomic marks. In

yeast, H2A.Z was associated with both active and inactive genes

(Raisner et al. 2005). In this study, H2A.Z was clearly associated

with active genes in mesendoderm cells but not in undifferentiated

ES cells. This shows the importance of considering the cellular

contexts when inferring the regulation functions of an epigenomic

mark.

Most of the epigenomic marks (all assayed except H3K36me3)

showed robust temporal changes in multiple genomic features,

including promoters, enhancers, gene bodies, and repeats. This

recurring theme can have large implications for studying gene

regulation. In the canonical view, certain modifications are in-

dicative of certain genomic features; for example, H3K27ac and

H3K4me1 are enhancer marks and H3K4me1 is a promoter mark.

This canonical view was built on the observation that these

modifications were a lot more abundant in certain genomic fea-

tures than others. This view made it tempting to ignore the regu-

latory roles of modification in places where it is not abundant.

However, the robust temporal changes of many modifications

in their noncanonical (low-abundance) regions, such as H3K27ac

in gene bodies, H3K4me1 in gene bodies and promoters, and

H3K4me3 in gene bodies and enhancers, indicate that they can

play regulatory roles in more genomic features than in the ca-

nonical view. Future experiments are needed to test this hypoth-

esis. Consistent with this new view, the temporal epigenomic

changes in low-abundance regions were sometimes correlated with

mRNA or ncRNA expression changes (Figs. 2, 6).

Another dilemma in the epigenomic field is as follows. On the

one hand, epigenomic changes are essential to organismal devel-

opment, supported by the fact that different cell types exhibit

clearly different epigenomic patterns (Hawkins et al. 2010; Ernst

et al. 2011). Thus, the epigenome is expected to regulate gene ex-

pression during development and differentiation (Hawkins et al.

2011). However, on the other hand, temporal epigenomic changes

during cell differentiation were reported to not correlate with gene

expression changes (Wu et al. 2011b). Our method and data allow

us to investigate this dilemma from a new perspective.

From the methodological perspective, GATE provides two

advantages. First, the unsupervised clustering summarizes the

combinatorial changes of multiple epigenomic marks. Previously,

one had to compare gene expression changes with every epi-

genomic mark one-by-one, resulting in inconclusive or even

conflicting results. This was because the association between gene

expression and an epigenomic mark may be confounded by other

epigenomic marks. GATE enables us to correlate gene expression

changes with the combinatorial changes of multiple epigenomic

marks. Second, GATE makes unsynchronized changes in different

parts of the genome comparable. This enables us to effectively pull

information together from different genomic segments with sim-

ilar but unsynchronized temporal changes.

Consistent with the previous erythroid differentiation study

(Wu et al. 2011b), temporal epigenomic changes did not correlate

with gene expression changes in several GATE clusters. These

clusters were all in promoters (Fig. 2, groups 5, 8, 12). However,

temporal epigenomic changes in enhancer-associated clusters

were clearly correlated with gene expression changes. In particular,

changes in DNA methylation alone were associated with ncRNA

expression change (group 6); changes that involve different com-

binations of DNA and histone modifications were associated with

both mRNA and ncRNA changes in different directions (Fig. 2,

groups 3, 7, 9); and changes in modifications on repeats were

predictive of repeat expression (groups 13, 14). Including non-

uniquely mapped reads into the analysis may impact the results on

repeat regions. These data suggest that the epigenome-mediated

Figure 6. A model for combinatorial epigenomic changes and gene expression. One to several combinatorial patterns (columns) were identified oneach genomic feature. The model-learned intensity levels for each epigenomic mark (input rows) in the undifferentiated state and the differentiated stateare color-coded, and the directions of change are marked by arrows. The corresponding temporal changes of mRNA and ncRNA expression are color-coded in a green-to-red scale (output rows).




gene regulation during cell differentiation, although clear in en-

hancers, may not be discernible in promoters, thus helping to re-

solve the hitherto mentioned dilemma.

Methods

The probabilistic model for analyzing temporal epigenomicdata (GATE) symbolsIndices are as follows: w, genomic segments; t, time points; m,epigenomic marks; and k, epigenomic clusters. Observed data areas follows: W, the number of genomic segments; M, the number ofepigenomic marks; T, the number of time points; and v, normal-ized sequence counts. Note that vw,t,m is the normalized sequencecount for epigenomic mark m in genomic segment w at time t. O isall the observed data. Hidden variables are as follows: Cw, clustermembership of the genomic segment w; H, activity states, takingvalues 0 or 1. Precomputed parameters are as follows: K, thenumber of epigenomic clusters. Model parameters are as follows:pk, the proportion of genomic segments in cluster k; bi,j, transitionprobability from state i to state j; l, the Poisson parameter foremission probabilities; and L, all the model parameters.

The model

The GATE model is a hierarchical model with two layers (Fig. 1B).The top layer is a FMM, in which each component of the mixturerepresents a cluster of genomic segments that share temporal epi-genomic patterns. The bottom layer models the time-course epi-genomic data in each cluster. Each cluster is modeled as a HMMwith the hidden states representing the changes of regulatory ac-tivities during a differentiation process, which emit the observedepigenomic data at each time point. Overall, GATE is a finitemixture of HMMs.

The top layer

The top layer FMM models the cluster memberships of everygenomic segment. The cluster membership of genomic segmentw is modeled as a categorical distribution with probability p =

(p1,. . .,pK):

Cw ; Categorical pð Þ; and P Cwð Þ= +Kk = 1P Cw = kð Þpk: ð1Þ

The HMM at the bottom layer

Given the cluster membership Cw, the potential changes of regu-latory activities for genomic segment w are modeled as a Markovchain. As a hidden variable, Hw,t 2 (0,1) represents the activity stateof genomic segment w at time t.

The transition probability matrix bCw

� �is written as

bCw

i,j = P Hw,t+1 = j Hw,t = i,Cw

�� , where i,j 2 0,1ð Þ: ð2Þ

The conditional probability of Hw given Cw is

P Hwj bCw ,Cw

� �= P Hw,1 Cwj� �YT�1

t = 1P Hw,t+1 Hw,t ,Cw

�� = P Hw,1 Cwj� �YT�1

t = 1bCw

Hw,t ,Hw,t + 1: ð3Þ

Given the hidden variable, the observed sequence count foreach epigenomic mark is modeled to follow a Poisson distribution(emission distribution). The Poisson parameter depends on thecluster membership and the hidden regulatory state.

vw,t,m ; Poisson lCw

Hw,t ,m

� �, where 1 # m # M,1 # w # W, 1# t # T

ð4Þ

Conditional on the cluster membership and the hidden var-iable, the different epigenomic marks are modeled as independent,and thus

P vwjCw, Hw; lCw� �

=YTt = 1

P vw,t��Cw, Hw,t ; lCw

� �

=YTt = 1

YMm = 1

P vw,t,m��Cw, Hw,t ; lCw

� �;

where vw = vw,1,vw,2; . . . ,vw,T� �

and

vw,t = vw,t,1,vw,t,2, . . . ,vw;t;M

� �: ð5Þ

Thus, a generative probabilistic model for all data has beenfully specified.

Likelihood function

Under model assumptions, the likelihood function of observeddata (O) is

P Ojb,l,pð Þ=YWw = 1

P vwjb,l,pð Þ

=YWw = 1

+K

Cw = 1

P vwjCw;bCw , lCw

� �P Cwð Þ

!

=YWw = 1

+K

Cw = 1

P Cwð Þ +Hw

½PðvwjCw,Hw;lCw Þ

PðHwjbCw ,CwÞ�!!

,

where b = b1, b2, . . . ,bK� �

, l = l1, l2, . . . , lK� �

: ð6Þ

Parameter inference

The hidden variables of interest (C, H) were estimated by maxi-mum likelihood estimation. We implemented a nested EM algo-rithm in which the transition and emission parameters of theHMM were estimated by a Baum-Welch algorithm (SupplementalFig. S1; Supplemental Methods).

Fitting data to the GATE model

For simulation data, the cluster number (K) was estimated by theBayesian information criteria (BIC):

BIC ¼ �2�Q LjLðfinalÞ� �

+ 2 3 K � 1 + K 3 M 3 2ð Þ 3 ln Wð Þ,where L ¼ b, l, pf g is the collection of all parameters:

For real data, we initial run the model with a relatively largecluster number (55), which was estimated from a previous study.The model-generated clusters were then merged into larger groupsbased on hierarchical clustering (Supplemental Fig. S3). We set thehidden state at the first time point as 0. We set bCw

1,0 = 1� bCw

1,1 = 0,because it is unlikely to make two switches of regulatory stateswithin this short differentiation time course.

Maintenance of ES cells

Undifferentiated mouse E14 ES cells were cultured under feeder-free conditions. ES cells were plated on gelatin-coated dishes with

Yu et al.



Dulbecco’s modified Eagle medium (DMEM; GIBCO), supple-mented with 15% heat-inactivated fetal bovine serum (FBS;GIBCO), 0.055 mM mercaptoethanol (2-ME; GIBCO), 2 mML-glutamine, 0.1 mM MEM nonessential amino acid, 5000 units/mL penicillin/streptomycin, and 1000 units/mL of LIF (MilliporeESG1107) at 37°C in 5% CO2 (Li et al. 2011).

Differentiation of ES cells into mesendoderm

Guided differentiation of ES cells was performed according to themethod previously described (Yasunaga et al. 2005). Briefly, 2 3

105 cells were seeded on Collagen IV–coated 10-cm dishes (BD, 08-774-33) in serum-free medium ESF-B (Itochu Corporation), sup-plemented with 0.1% BSA, 50 mM 2-ME, and 10 ng/mL Activin A(R&D Systems). The culture medium was changed every day.

Reverse transcription polymerase chain reaction

Total RNA was extracted from cells 0, 4, and 6 d after induction ofdifferentiation with TRIzol Reagent (Invitrogen, 15596-026)according to manufacturer’s protocol. First-strand cDNA was pre-pared with M-MLV Synthesis System (New England Biolabs). Beta-actin was used as a control. Pluripotency and lineage-specificmarker genes were assayed by the Applied Biosystems 7900HT FastReal-Time PCR System. Primer sequences are listed in Supple-mental Table S5. Gene expression levels were normalized to theexpression level of beta-actin. Fold changes of gene expressionlevels were calculated between day 4 and day 0 and between day 6and day 0.

Immunostaining

A total of 10,000–20,000 cells were seeded on Collagen IV–coated35-mm dishes (Ibidi 45074) in the medium used for guided dif-ferentiation (ESF-B supplemented with 0.1% BSA, 50 mM 2-ME,and 10 ng/mL Activin A). Cells were fixed in 4% paraformaldehyde.Primary antibodies against GSC (Origene, TA500087) and Sox17(Millipore 09-038) were mixed and applied to the fixed cells for 2 hat 37°C. The goat anti-mouse IgG antibody conjugated with Alexa568 (Invitrogen A-11031) and the goat anti-rabbit IgG antibodyconjugated with Alexa 488 (Invitrogen A-11034) were sequentiallyapplied to the samples, each for 2 h at 37°C, as secondary antibodies.Cellular nuclei were stained by Hoechst 33342 (Invitrogen, H3570)for 15 min at room temperature. Images were obtained using theLSM 700 microscope (Zeiss).

Chromatin immunoprecipitation

Cells were fixed with 1% formaldehyde for 10 min at roomtemperature. Fixation was inactivated by the addition of 125mM glycine. Cells were scraped off of dishes and collected bycentrifugation. Cross-linked chromatin–DNA complexes wereisolated from the nuclei lysis buffer and then sonicated intofragments of a size range between 350 and 600 nt. Specific anti-bodies listed below were incubated with the solubilized DNAfragments at 4°C overnight.

Antibodies used in this work are as follows: anti-histoneH2A.Z antibody, ChIP Grade (Abcam, ab4174); anti-histone H3(mono methyl K4) antibody, ChIP Grade (ab8895); anti-histoneH3 (di methyl K4) antibody [Y47], ChIP Grade (ab32356); anti-histoneH3 (tri methyl K4) antibody, ChIP Grade (ab1012); anti-histone H3 (trimethyl K4) antibody, ChIP Grade (ab8580); anti-histone H3 (trimethyl K36) antibody, ChIP Grade (ab9050); anti-histone H3(acetyl K27) antibody, ChIP Grade (ab4729); anti-H3K27me3 an-tibody (Millipore, 07-449); and a monoclonal antibody against5-methylcytindine (Eurogentec, bi-mecy-0100).

Antibody–chromatin complexes were captured by proteinA/G Agarose beads (Pierce) and eluted with 1% SDS after extensivewashing. The cross-link between DNA and chromatin proteins wasreversed by incubation in 20 mM NaCl overnight at 65°C. DNAwas purified by QIAquick PCR Purification Kit (Qiagen 28106) anddissolved into 30 mL TE buffer per immunoprecipitation.

MRE-seq, MeDIP-seq, and 5-hmC-seq

MRE-seq and MeDIP-seq were performed according to the methodpreviously described (Maunakea et al. 2010). Sample DNA wasdigested in parallel using HpaII, Hin6I, SsiI (Fermentas), andHpyCH4IV (New England Biolabs) before deep sequencing.

5-hmC-seq was performed according to the method pre-viously described (Song et al. 2011). 5-hmC was chemically labeledas selected. Sequencing libraries were constructed using the sameprotocol as ChIP-seq (Illumina 2010a).

Small RNA sequencing

Total RNA was purified with TRIzol Reagent (Invitrogen 15596-026) and used as an input to generate a small RNA library usingTrue-seq small RNA kit (Illumina RS-200-0012). The RNA 39

adapters in this kit were specifically modified to target miRNAs andother small RNAs that have a 39 hydroxyl group resulting fromenzymatic cleavage by Dicer or other RNA processing enzymes.Library products ranging from 145–160 nt were collected andamplified. The libraries were quantitated by qPCR, and sub-sequently sequenced on a HiSeq2000 sequencer using TruSeq SBSsequencing kit version 2 and analyzed with pipeline version 1.8(Illumina).

Data accessAll sequencing data are accessible from the NCBI Gene ExpressionOmnibus (GEO) (http://www.ncbi.nlm.nih.gov/geo/) under Super-Series accession no. GSE38596.

AcknowledgmentsWe thank Dr. Alvaro Hernandez for useful discussions. This workwas supported by NIH DP2OD007417, NSF DBI 0845823, SloanResearch Fellowship to S.Z., March of Dimes Foundation, EdwardJr. Mallinckrodt Foundation to T.W., NIH R01HG006827 to C.H.,and American Cancer Society Illinois 207962 to T.T.

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Erratum

Genome Research 23: 352–364 (2013)

Spatiotemporal clustering of the epigenome reveals rules of dynamic gene regulationPengfei Yu, Shu Xiao, Xiaoyun Xin, Chun-Xiao Song, Wei Huang, Darina McDee, Tetsuya Tanaka, Ting Wang,Chuan He, and Sheng Zhong

The website address of the GATE program used in this article (see page 354, lefthand column, secondparagraph) is no longer valid. The new URL for the program is: http://systemsbio.ucsd.edu/GATE/.

The authors apologize for any confusion this may have caused.

23:747 � 2013, Published by Cold Spring Harbor Laboratory Press; ISSN 1088-9051/13; www.genome.org Genome Research 747www.genome.org

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